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MHT CET20228 Aug 2022Evening ShiftMathematicsDifferential EquationsActual

The solution of the differential equation e ^ ( d y ~d x ) =x+1 ; y(0)=5 , x (-1, )

Options

  1. A(x-1) (x+1)-x-5=y
  2. B(x+1) (x+1)+x+5=y
  3. C(x-1) (x+1)+x-5=y
  4. D(x+1) (x+1)-x+5=y

Correct answer

D. (x+1) (x+1)-x+5=y

Step-by-step solution

aligned & e ^ d y ~d x =x+1 & d y ~d x = _ e (x+1) & d y= _ e (x+1) d x & y=(x+1) _ e (x+1)-(x+1)+C [integrating by parts] & putting x=0 and y=5 we get C=6 & y=(x+1) _ e (x+1)-x+5 aligned

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